相关论文: Modified Filon-Clenshaw-Curtis rules for oscillato…

This paper extends the earlier work on an oscillating error correction technique. Specifically, it extends the design to include further corrections, by adding new layers to the classifier through a branching method. This technique is still…

We study a new simple quadrature rule based on integrating a $C^1$ quadratic spline quasi-interpolant on a bounded interval. We give nodes and weights for uniform and non-uniform partitions. We also give error estimates for smooth functions…

We introduce a new method for evaluating the oscillatory integrals which describe natural interference patterns. As an illustrative example of contemporary interest, we consider astrophysical plasma lensing of coherent sources like pulsars…

The double exponential formula was introduced for calculating definite integrals with singular point oscillation functions and Fourier-integrals. The double exponential transformation is not only useful for numerical computations but it is…

It is well known that second order linear ordinary differential equations with slowly varying coefficients admit slowly varying phase functions. This observation is the basis of the Liouville-Green method and many other techniques for the…

We present a new efficient method for computing the non-linearity parameters of the higher order correlation functions of local type curvature perturbations in inflation models having a $\cal N$-component scalar field, focusing on the…

We study stochastic optimization from a joint continuous-discrete point of view. Starting from a second-order stochastic differential equation interpreted as a noisy accelerated gradient flow, we discretize the dynamics by a fully implicit…

In this paper, we report new results on a novel Ising machine technology for solving combinatorial optimization problems using networks of coupled self-sustaining oscillators. Specifically, we present several working hardware prototypes…

We describe an algorithm for the numerical solution of second order linear differential equations in the highly-oscillatory regime. It is founded on the recent observation that the solutions of equations of this type can be accurately…

Exponential time differencing methods is a power tool for high-performance numerical simulation of computationally challenging problems in condensed matter physics, fluid dynamics, chemical and biological physics, where mathematical models…

In this paper, we consider the Gauss quadrature formulae corresponding to some modifications of anyone of the four Chebyshev weights, considered by Gautschi and Li in \cite{gauli}. As it is well known, in the case of analytic integrands,…

We present a new time-stepping algorithm for nonlinear PDEs that exhibit scale separation in time. Our scheme combines asymptotic techniques (which are inexpensive but can have insufficient accuracy) with parallel-in-time methods (which,…

We study the Cowling approximation by analytical means as applied to a system of linear differential equations arising from models of non-radial stellar pulsation. We consider various asymptotic cases, including those of high harmonic…

In a posteriori error analysis, the relationship between error and estimator is usually spoiled by so-called oscillation terms, which cannot be bounded by the error. In order to remedy, we devise a new approach where the oscillation has the…

In this paper we present a novel particle method for the Vlasov--Poisson equation. Unlike in conventional particle methods, the particles are not interpreted as point charges, but as point values of the distribution function. In between the…

This work is concerned with practical stabilization of nonlinear systems by means of inf-convolution-based sample-and-hold control. It is a fairly general stabilization technique based on a generic non-smooth control Lyapunov function (CLF)…

This paper introduces the Non-linear Partition of Unity Method, a novel technique integrating Radial Basis Function interpolation and Weighted Essentially Non-Oscillatory algorithms. It addresses challenges in high-accuracy approximations,…

We introduce a new non-resonant low-regularity integrator for the cubic nonlinear Schr\"odinger equation (NLSE) allowing for long-time error estimates which are optimal in the sense of the underlying PDE. The main idea thereby lies in…

In this paper we demonstrate that the numerical method of steepest descent fails when applied in a straight forward fashion to the most commonly occurring highly oscillatory integrals in scattering theory. Through a polar change of…

In this study, the standard IEEE 754 2008 and modulo-based floor functions for rounding non-integers have been presented. Their effects on the accuracy of the bilinear interpolation algorithm have been demonstrated. The improved floor uses…